Question 21
Find the number of polynomials $f(x) = a x^3 + b x$ that satisfy the following conditions:
(1) $a, b \in \{1, 2, \dots, 2013\}$;
(2) the difference of any two numbers among $f(1)$, $f(2)$, $\dots$, $f(2013)$ is not a multiple of $2013$.
(1) $a, b \in \{1, 2, \dots, 2013\}$;
(2) the difference of any two numbers among $f(1)$, $f(2)$, $\dots$, $f(2013)$ is not a multiple of $2013$.